Iteration of meromorphic functions
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In this paper, the authors describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions, and some aspects where the transcendental case is analogous to the rational case are treated rather briefly here.Abstract:
This paper attempts to describe some of the results obtained in the iteration theory of transcendental meromorphic functions, not excluding the case of entire functions. The reader is not expected to be familiar with the iteration theory of rational functions. On the other hand, some aspects where the transcendental case is analogous to the rational case are treated rather briefly here. For example, we introduce the different types of components of the Fatou set that occur in the iteration of rational functions but omit a detailed description of these types. Instead, we concentrate on the types of components that are special to transcendental functions (Baker domains and wandering domains).read more
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On the Hausdorff measure of the Julia set and the escaping set of entire functions with regularly growing maximum modulus
TL;DR: In this article, it was shown that the Hausdorff measure of the escaping set and the Julia set of an entire function f is infinite with respect to certain gauge functions, provided that f is outside of the Eremenko-Lyubich class, and that the maximum modulus M(r, f) satisfies a certain regularity condition.
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TL;DR: In this paper , it was shown that the set of non-recurrent parameters with Lebesgue measure zero has no escaping parameters, which complements a result of Qiu from 1994.
RESEARCH ARTICLE Elliptic functions with critical orbits approaching inflnity
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DYNAMICS OF f‚tanh(e z ) : ‚ 2R n f0gg
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Dimensions of non-autonomous meromorphic functions of finite order
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References
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TL;DR: A can is a can made of a steel sheet the surface of which is coated with a three-layered chromium coating, consisting of a metallic chromium coated, a crystalline chromium oxide coating and a non-crystalline hydrated chromiumoxide coating in this order.